SI Prefixes on the AP Physics Equation Sheet

All four AP Physics booklets print the same prefixes table, and it has nine rows: tera, giga, mega, kilo, centi, milli, micro, nano and pico. It runs from a factor of ten to the twelfth down to ten to the minus twelfth. Deci, deka and hecto are not on it, and neither is anything smaller than pico.

Read off the PREFIXES table in the Table of Information appendix of all four Course and Exam Descriptions, effective Fall 2024: AP Physics 1 (printed appendix page 211), AP Physics 2 (page 218), AP Physics C: Mechanics (page 204) and AP Physics C: Electricity and Magnetism (page 178). The table is identical in all four.

The prefixes table, exactly as the booklet prints it

The PREFIXES table is identical in all four Course and Exam Description appendices: AP Physics 1, AP Physics 2, AP Physics C: Mechanics and AP Physics C: Electricity and Magnetism. Same nine rows, same three columns, same order, top to bottom largest first.

FactorPrefixSymbol
101210^{12}teraT
10910^{9}gigaG
10610^{6}megaM
10310^{3}kilok
10−210^{-2}centic
10−310^{-3}millim
10−610^{-6}microμ\mu
10−910^{-9}nanon
10−1210^{-12}picop

Nine rows. Count them if you are quoting a number somewhere, because it is the kind of figure people get wrong from memory: the table looks like it should have ten or twelve entries and it does not.

The span is symmetric. Tera is 101210^{12}, pico is 10−1210^{-12}, so the table covers twenty four orders of magnitude with the unit itself sitting in the middle.

One more structural detail worth noticing, because it explains why the table feels lopsided when you read it. Every exponent in the table is a multiple of three except one. Centi, at 10−210^{-2}, is the only entry that is not, and it is there because centimeters and g/cm3\text{g}/\text{cm}^3 are unavoidable in a physics classroom, not because it fits the pattern.

What the AP table leaves out

Between kilo at 10310^{3} and centi at 10−210^{-2} the printed table simply stops. Nothing sits in that gap. Three real SI prefixes live there and none of them appear on the AP sheet:

  • hecto, 10210^{2}, symbol h
  • deka, 10110^{1}, symbol da
  • deci, 10−110^{-1}, symbol d

Deci is the one that catches people, because a decimeter and a deciliter are ordinary words outside physics class. The AP booklet does not print it.

At the two ends, the table stops at tera and pico. SI keeps going in both directions, with peta, exa, zetta and yotta above tera and femto, atto, zepto and yocto below pico. None of those are printed either. This matters most for femto, 10−1510^{-15}: nuclear sizes are quoted in femtometers in a lot of outside reading, and AP Physics 2's modern physics content never needs the prefix because the booklet works in meters and electron volts instead.

Do not read the omissions as a rule about what the exam can ask. They are a statement about what the booklet hands you, nothing more. A question is free to write a number in whatever form it likes and expect you to work with it.

Every prefix symbol on this table means something else somewhere in the same booklet

This is the part that actually costs points, and it is the reason a prefix table is worth reading rather than glancing at. Take the four booklets together. All nine of the prefix symbols are also used, in the same appendix, for a physical quantity or a unit. Not most of them. All nine.

Prefix symbolAs a prefixAlso printed as
Ttera, 101210^{12}the unit symbol for tesla, and TT for period, and TT for temperature
Ggiga, 10910^{9}GG, the universal gravitational constant
Mmega, 10610^{6}MM for mass, and MM for magnification
kkilo, 10310^{3}kk for spring constant, kk for the Coulomb constant, kk for thermal conductivity
ccenti, 10−210^{-2}cc, the speed of light, and cc for specific heat
mmilli, 10−310^{-3}the unit symbol for meter, and mm for mass
μ\mumicro, 10−610^{-6}μ\mu for coefficient of friction, and μ0\mu_0 for vacuum permeability
nnano, 10−910^{-9}nn for index of refraction, and nn for number of moles
ppico, 10−1210^{-12}pp for momentum

Two of those are worse than the rest.

m. Lowercase m is milli, and it is the unit symbol for meter, and it is the variable for mass. So "mm" is millimeters and not mass times meters, and "mm = 5.0 mg" is a mass of five milligrams. Context is the only thing separating them, and the sheet gives you no help.

T. Uppercase T is tera, the unit symbol for tesla, the variable for period on the mechanics list, and the variable for temperature on the thermal and modern physics lists. In a magnetism problem "0.50 T" is half a tesla; in an oscillations problem "TT = 0.50" is a half second period.

The rule that gets you through it: prefixes only ever appear glued to the front of a unit symbol, never on their own and never in italics. The AP booklet italicizes variables and sets unit symbols upright. On your own paper, keep prefixes attached to their unit and you will not confuse yourself.

Converting with a prefix, and the exponent trap that follows

A prefix is a multiplication, so converting is a substitution and nothing more. Replace the prefix with its power of ten:

2.5 km=2.5×103 m2.5\ \text{km} = 2.5 \times 10^{3}\ \text{m}
470 nm=470×10−9 m=4.70×10−7 m470\ \text{nm} = 470 \times 10^{-9}\ \text{m} = 4.70 \times 10^{-7}\ \text{m}
15 μC=15×10−6 C=1.5×10−5 C15\ \mu\text{C} = 15 \times 10^{-6}\ \text{C} = 1.5 \times 10^{-5}\ \text{C}

That direction is easy. The trap is what happens when the prefixed unit is raised to a power, because the prefix goes up with it.

1 cm2=(10−2 m)2=10−4 m21\ \text{cm}^2 = \left(10^{-2}\ \text{m}\right)^2 = 10^{-4}\ \text{m}^2
1 cm3=(10−2 m)3=10−6 m31\ \text{cm}^3 = \left(10^{-2}\ \text{m}\right)^3 = 10^{-6}\ \text{m}^3

So a density quoted as 1.0 g/cm31.0\ \text{g}/\text{cm}^3, which is water, is 1000 kg/m31000\ \text{kg}/\text{m}^3 and not 1 kg/m31\ \text{kg}/\text{m}^3 or 10 kg/m310\ \text{kg}/\text{m}^3. Work it through once and the factor stops surprising you: one gram is 10−310^{-3} kg, one cubic centimeter is 10−610^{-6} cubic meters, and 10−3/10−6=10310^{-3}/10^{-6} = 10^{3}.

The safe habit for an AP problem is to strip every prefix on the first line of your work, before any physics happens. Convert to base SI units, solve, then put a prefix back only if the answer wants one. Every equation on the sheet assumes base units, and nothing on the sheet reminds you of that.

Which prefixes actually turn up on each exam

The table is the same on all four sheets, but the prefixes you meet are not, because the quantities differ.

AP Physics 1. Mostly centi and kilo, and milli for small masses and lengths. Springs in N/m\text{N}/\text{m}, distances in cm, masses given in grams. Fluids brings densities in kg/m3\text{kg}/\text{m}^3 against everyday values quoted in g/cm3\text{g}/\text{cm}^3, which is the cubed prefix trap again.

AP Physics 2. Nano for wavelengths of visible light, micro and nano and pico for charges and capacitances, kilo and mega for resistances. Optics questions lean on nm hard: the sheet's own hc=1240 eV⋅nmhc = 1240\ \text{eV} \cdot \text{nm} is written in nanometers specifically so you can divide by a wavelength in nm and read off an energy in electron volts without converting anything.

AP Physics C: Mechanics. Much like Physics 1. Centi, kilo, milli.

AP Physics C: Electricity and Magnetism. Micro, nano and pico for charge and capacitance, milli and micro for currents, kilo and mega for resistance. The C: E&M booklet is the only one of the four whose unit symbols table prints henry, so millihenry is a unit you can meet there and nowhere else on the AP sheets.

Reading the table on exam day

The prefixes table sits on the first page of the Table of Information, next to the constants box, on all four booklets. You get it in the exam room. There is nothing to memorize here and no advantage in having memorized it.

What is worth practicing is the substitution, not the recall. If you have to stop and think about whether nano is 10−910^{-9} or 10−1210^{-12}, you have already lost more time to the lookup than the conversion is worth. Reach for the sheet, read the row, move on.

The one thing the sheet cannot do for you is catch a prefix you failed to notice. A problem that says "a 2.0 μF2.0\ \mu\text{F} capacitor" and an answer computed with 2.02.0 farads differ by a factor of a million, and the arithmetic will look perfectly reasonable the whole way through. Circle the prefixes when you first read a problem.

Density given in grams per cubic centimeter

A block has a density of 2.7 g/cm32.7\ \text{g}/\text{cm}^3. Express this in kg/m3\text{kg}/\text{m}^3, then find the mass of a cube of this material 5.0 cm on a side.

  1. Convert the density first. One gram is 10−310^{-3} kg. One cubic centimeter is (10−2 m)3=10−6 m3\left(10^{-2}\ \text{m}\right)^3 = 10^{-6}\ \text{m}^3.

  2. ρ=2.7×10−3 kg10−6 m3=2.7×103 kg/m3\rho = 2.7 \times \dfrac{10^{-3}\ \text{kg}}{10^{-6}\ \text{m}^3} = 2.7 \times 10^{3}\ \text{kg}/\text{m}^3

  3. The prefix on the volume moved by three powers of ten, not one, because centi was cubed. That is the whole trap.

  4. Now the volume of the cube. A side of 5.0 cm is 5.0×10−25.0 \times 10^{-2} m.

  5. V=(5.0×10−2 m)3=1.25×10−4 m3V = \left(5.0 \times 10^{-2}\ \text{m}\right)^3 = 1.25 \times 10^{-4}\ \text{m}^3

  6. m=ρV=(2.7×103)(1.25×10−4)=0.3375 kgm = \rho V = \left(2.7 \times 10^{3}\right)\left(1.25 \times 10^{-4}\right) = 0.3375\ \text{kg}

  7. To two significant figures, m=0.34m = 0.34 kg, or 340 g.

ρ=2.7×103 kg/m3\rho = 2.7 \times 10^{3}\ \text{kg}/\text{m}^3 and m=0.34m = 0.34 kg.

Photon energy straight from a wavelength in nanometers

Green light has a wavelength of 550 nm. Use the AP Physics 2 constants box to find the photon energy in electron volts, then in joules.

  1. The AP Physics 2 Table of Information prints hc=1240 eV⋅nmhc = 1240\ \text{eV} \cdot \text{nm}. That form exists so a wavelength already in nanometers needs no conversion at all.

  2. E=hcλ=1240 eV⋅nm550 nm=2.2545 eVE = \dfrac{hc}{\lambda} = \dfrac{1240\ \text{eV} \cdot \text{nm}}{550\ \text{nm}} = 2.2545\ \text{eV}

  3. To two significant figures, E=2.3E = 2.3 eV.

  4. For joules, use the printed conversion 1 eV=1.60×10−19 J1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}.

  5. E=2.2545×1.60×10−19=3.607×10−19 JE = 2.2545 \times 1.60 \times 10^{-19} = 3.607 \times 10^{-19}\ \text{J}

  6. To two significant figures, E=3.6×10−19E = 3.6 \times 10^{-19} J.

  7. Check it the long way to see what the nm form saved you. Converting first, λ=550×10−9=5.50×10−7\lambda = 550 \times 10^{-9} = 5.50 \times 10^{-7} m, and with hc=1.99×10−25 J⋅mhc = 1.99 \times 10^{-25}\ \text{J} \cdot \text{m} from the same box, E=1.99×10−25/5.50×10−7=3.618×10−19 JE = 1.99 \times 10^{-25} / 5.50 \times 10^{-7} = 3.618 \times 10^{-19}\ \text{J}. Same answer to two figures.

E=2.3E = 2.3 eV, which is 3.6×10−193.6 \times 10^{-19} J.

Frequently asked questions

How many SI prefixes are on the AP Physics equation sheet?

Nine. The PREFIXES table in the Table of Information lists tera, giga, mega, kilo, centi, milli, micro, nano and pico, with their factors from ten to the twelfth down to ten to the minus twelfth and their symbols T, G, M, k, c, m, mu, n and p. The same nine rows appear in all four booklets: AP Physics 1, AP Physics 2, AP Physics C: Mechanics and AP Physics C: Electricity and Magnetism.

Is deci on the AP Physics prefixes table?

No. The AP Physics prefixes table jumps straight from kilo at ten to the third to centi at ten to the minus second, with nothing printed in between. Deci (ten to the minus first), deka (ten to the first) and hecto (ten to the second) are all real SI prefixes and none of the three is printed in the AP booklet. That does not stop a question from using one, so read the units on every given quantity rather than assuming everything comes in a prefix you were handed.

Do I need to memorize the metric prefixes for AP Physics?

No. The prefixes table is printed in the Table of Information that comes with the exam, on the same page as the constants and the trigonometry values. What you should practice is using it quickly: substituting the power of ten for the prefix on the first line of your work, before any physics, and remembering that a squared or cubed prefixed unit raises the power of ten too.

Why is one centimeter cubed equal to ten to the minus six cubic meters and not ten to the minus two?

Because the prefix is part of the unit being cubed, not a separate factor tacked on. One centimeter is ten to the minus second meters, so one cubic centimeter is that quantity cubed, which is ten to the minus sixth cubic meters. The same logic gives ten to the minus fourth square meters for one square centimeter. This is why a density of one gram per cubic centimeter, which is water, works out to one thousand kilograms per cubic meter.

What is the difference between M and m on the AP Physics sheet?

Uppercase M is the prefix mega, a factor of ten to the sixth, and it is also used as a variable for mass in the rotation equations. Lowercase m is the prefix milli, a factor of ten to the minus third, and it is also the unit symbol for meter and the usual variable for mass. Prefixes only appear attached to the front of a unit symbol, so MW is megawatts and mW is milliwatts, while an italic m standing alone is a mass.

Is femto or pico the smallest prefix on the AP sheet?

Pico, ten to the minus twelfth, is the smallest prefix printed on the AP Physics sheet. Femto, ten to the minus fifteenth, is not on the table in any of the four booklets, even though nuclear distances are often quoted in femtometers outside of AP materials. The largest printed prefix is tera, ten to the twelfth, so the table spans twenty four orders of magnitude and stops.

Are the prefixes different on the AP Physics C sheet?

No. The prefixes table is the same in all four Course and Exam Descriptions, including both Physics C booklets: nine rows, tera through pico, with centi as the only exponent that is not a multiple of three. The constants boxes and the unit symbol tables do differ between the four courses, but the prefixes do not.